Question

integral[7 sqrt 2/2,0]sqrt(49+x^2) dx

Answer 1

using trig substitutions, you can show that

integral sqrt(a^2 + x^2)
= 1/2 (x*sqrt(a^2+x^2) + a^2 log(x + sqrt(a^2+x^2)))
= arcsinh(x/a)